1. Field of the Invention
The present invention generally relates to analog-to-digital (A/D) conversion techniques. More particularly, the present invention pertains to the digital implementation of a finite-impulse-response (FIR) low-pass filter to suppress the out-of-band quantization noise from a particular class of A/D converters known as noise-shaping coders.
2. Description of the Prior Art
Before any analog signal can be processed through digital means, a translation of the analog signal to a sampled-time quantized digital representation must be performed. Such a translation is normally accomplished utilizing an analog-to-digital (A/D) converter. Functionally, a linear A/D converter is a device that accepts an analog voltage at its input terminals and yields a set of digitally-coded outputs whose magnitude is proportional to the input voltage. Numerous A/D converter techniques are known in the art. A summary of some of the more widely known A/D conversion techniques is given in B.M. Gordon, "Linear Electronic Analog-Digital Conversion Architectures, Their Origins, Parameters, Limitations, and Applications," IEEE Transactions on Circuits and Systems, Vol. CAS-25, No. 7, July 1978, pp. 391-418.
Digital processing of audio and video signals necessitates the use of an A/D converter capable of high sampling rates (8 kHz-500 kHz) and high resolution (in excess of 10 bits). This combination of requirements rules out many A/D conversion techniques, including those frequently employed in integrated circuits (ICs). One conversion method that does meet both the sampling rate and resolution requirements, while being compatible with existing IC processes, is a class of A/D converter techniques known as noise-shaping coders.
A noise-shaping coder is an A/D converter which allows the use of a fewer number of quantizer levels as compared to a standard flash-type A/D converter. The term "noise-shaping" originates from the observation that placing a quantizer in a feedback loop with a filter shapes the spectrum of the modulation noise. Noiseshaping coders typically incorporate oversampling of the input signal, employing a feedback network to shape the in-band quantization noise, low-pass filtering the out-of-band quantization noise, and decimating the output at a rate equal to the oversampling rate Oversampling and decimation is often used to avoid high-speed digital signal processing in stages subsequent to the A/D. An example of a 1-bit quantizer noise-shaping coder is a sigma-delta modulator (SDM), as described in detail by R. Steele, Delta Modulation Systems, New York: John Wiley, 1975, pp. 17-20.
It is well known that simple oversampling, as applied to a multi-level quantizer, suppresses the quantization noise by a suppression factor S of: EQU S(dB)=10 log .sub.10 N
where N, the oversampling factor, is equal to the ratio of the sampling frequency to the Nyquist sampling frequency of the signal. Thus, a signal must be oversampled by a factor of N=4 in order to gain one additional bit (6 dB) of resolution. By employing a noise-shaping feedback path in the quantizer along with this oversampling technique, the quantization noise floor for frequencies less than one-half the Nyquist sampling frequency can be suppressed by a factor: EQU S(dB)=10 (2K+1) log .sub.10 N
where K is the order of the noise-shaping network. (See S. K. Tewksbury, "Oversampled, Linear Predictive and Noise-Shaping Coders of Order N&gt;1", IEEE Transactions on Circuits and Systems, Vol. CAS-25, No. 7, July 1978, pp. 436-447, for analysis of equations.) Hence, a fairly simple noise-shaping network, i.e., K=1 or 2, yields a significant improvement in the in-band noise performance of the A/D converter. Furthermore, by choosing K=2 and N=100, a 1-bit quantizer can achieve 12 bits of resolution and still be readily implemented in silicon.
The noise-shaping coder introduces frequency weighting of the quantized noise power spectral density, as seen by the following equation for the spectral density for a first order Sigma-Delta modulator: ##EQU1## where .sigma. is the quantization step size and .tau. is the sampling period. The quantization noise N(f) is suppressed the most at low frequencies where the loop gain of the feedback path is the highest. This reduction of in-band low frequency noise is accompanied by an increase in out-of-band high frequency noise. In order to achieve the aforementioned improvements in resolution, it is necessary to adequately suppress the out-of-band quantization noise prior to decimation. A low-pass filter with a very sharp cut-off must be utilized at the output of the quantizer to prevent the quantization noise from aliasing back into the signal band.
Digital finite-impulse-response (FIR) filters are well-suited for implementation in integrated circuitry. The conventional high-speed/high-order (non-decimating) FIR filter comprises a tapped delay line, a means for weighting the outputs of those taps (such as a multiplier), and a means for summing all the delayed and weighted signal samples (such as an accumulator). For an L-tap filter, L cascaded multiplier-accumulators (MACs) are generally required. This approach is most reasonable when the sampling rate fS is much less than the MAC maximum operating range.
The implementation of such an FIR filter presents several drawbacks. First, the use of multipliers places an upper limit on the operating speed of the A/D converter. To achieve speeds compatible with audio and video signals, the use of full multiply/accumulate functions in a 384 tap FIR low-pass filter would require digital signal processing (DSP) speeds in excess of 12.2 GHz for sampling rates of 32 MHz, which is presently not practical with today's DSP technology.
Secondly, in order to achieve the resolution necessary for high quality video signals, an FIR filter must have a large number of filter taps, e.g., 384 filter taps. Such a number of MACs becomes prohibitively large and expensive to implement in ICs. For example, the implementation of a 384-tap video-speed FIR filter becomes a formidable task in terms of the integration size/expense/resolution trade-off.
Third, as mentioned above, the out-of-band quantization noise power can be reduced by using a lowpass filter having a sharp cutoff response. Again, there is a significant design trade-off between digital filter complexity and signal-to-quantization noise ratio (SQNR) performance.
A need, therefore, exists to provide a high-speed, high resolution, low noise, digital filtering technique which remains compatible with present integrated circuit size and cost goals.